Yahoo Answers: Answers and Comments for Find the volume of the largest cube contained the sphere? given: radius = 3cm.? [Mathematics]
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From reginah
enUS
Thu, 04 Sep 2008 04:50:41 +0000
3
Yahoo Answers: Answers and Comments for Find the volume of the largest cube contained the sphere? given: radius = 3cm.? [Mathematics]
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From yo_brooz: The radius of the sphere = the distance from t...
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Thu, 04 Sep 2008 12:11:21 +0000
The radius of the sphere = the distance from the centre of the cube to a corner.
let 'x' be the length of one side of the cube
the distance from the centre of a face to the corner = x/√2
therefore the distance from the centre of the cube to a corner
= (x/√2)^2 + (x/2)^2 all square rooted
= √(3x^2/4)
the radius is 3cm
3 = √(3x^2/4)
9 = 3x^2/4
36 = 3x^2
x = √12
The volume is 12√12 = 24√3 cm^3
or approximately 41.57cm^3

From vramasudheer: if you consider a single view of that sphere, ...
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Thu, 04 Sep 2008 12:24:10 +0000
if you consider a single view of that sphere, the largest square contained in that is the one whose diagonal is equal to the diameter of the circle.
so the diagonal of the square is 6 cm.
so, side^2+side^2 = diagonal^2
2 Side^2 = 36
side = 3√2
so the largest cube contained in the sphere is same as the largest square in the circle,
so cube side is 3√2, so volume = (3√2)^3 = 54√2 = 76.367 cm^3